Muamba collapsed suffering a cardiac arrest during Bolton's FA Cup sixth-round tie on Saturday evening. After medics from both clubs tried to revive him on the pitch for several minutes, the 23-year-old was taken to The London Chest Hospital where he remains in intensive care.
Soon after Muamba left the pitch on a stretcher, referee Howard Webb abandoned the match, which had been locked at 1-1 with 41 minutes played.
A short statement via the club's official Twitter account reads: "Bolton Wanderers can confirm that Tuesday evening's Barclays Premier League fixture against Aston Villa has been postponed.
"The Club would like to thank Aston Villa and the Premier League for their kind support and understanding at this time."
As yet, no date has been given for when the fixture at Villa Park will rescheduled.